The problem addressed here is the compensation of remotely sensed multi- and hyperspectral images in the solar reflective spectral regime (λ<3000 nm) for the transmission losses and scattering effects of the intervening atmosphere. The problem is illustrated in FIG. 1 for a pixel containing vegetation as viewed from a space-based sensor. A number of large spectral depressions are seen which are primarily due to absorption by gaseous water and to a lesser extent by carbon dioxide and oxygen. Below 700 nm, the observed reflectance exceeds the actual reflectance; this is due to atmospheric scattering by aerosols and molecules. The apparent reflectance at the sensor is well represented byρj(λ)=A(λ)+B(λ)ρjo(λ)+C(λ)<ρ(λ)>,  (1)where ρj is the observed reflectance (the radiance normalized by the surface normal component of the solar flux) for the j'th pixel at a spectral band centered at wavelength λ, ρjo is the actual surface reflectance, <ρ> is a spatially averaged surface reflectance, and A, B, and C are coefficients representing the transmission and scattering effects of the atmosphere. The first coefficient, A, accounts for light which never encounters the surface and is scattered and absorbed within the atmosphere. The second, B, accounts for the sun-surface-sensor path transmittance loss. The third, C, accounts for the adjacency effect which is the cross talk between pixels induced by atmospheric scattering. The length scale of the adjacency effect is typically of order ˜0.5 km, thus <ρ> is a slowly varying function of position within a large image. It is noted that B and C also have a weak dependence on <ρ> through light that reflects off the surface and is scattered back to the surface by the atmosphere.
The aim of atmospheric compensation is to determine A, B, C and <ρ> by some means in order to invert Eq(1) to retrieve the actual surface reflectance, ρjo. The prior art is embodied in various methods described in the literature and summarized below.
The simplest and computationally fastest prior art methods for atmospheric correction are the “Empirical Line Method” (ELM) and variants thereof, which may be found in the ENVI (Environment for Visualizing Images) software package of Research Systems, Inc. The ELM assumes that the radiance image contains some pixels of known reflectance, and also that the radiance and reflectance values for each wavelength channel of the sensor are linearly related, in the approximation that A, B, C and <ρ> are constants of the image. Therefore, the image can be converted to reflectance by applying a simple gain and offset derived from the known pixels. This method is however not generally applicable, as in-scene known reflectances are often not available. In variants of the ELM, approximate gain and offset values are generated using pixels in the image that are treated as if their spectra were known. For example, in the Flat Field Method a single bright pixel is taken as having a spectrally flat reflectance and the offset is taken as zero; accordingly, dividing the image pixel spectra by the bright pixel spectrum yields approximate relative reflectances. In the Internal Average Relative Reflectance method this procedure is followed using a scene-average spectrum rather than a single bright pixel spectrum. In general, neither the Flat Field Method nor the Average Relative Reflectance methods are very accurate.
More sophisticated prior art methods are based on first-principles computer modeling. These methods require extensive, and often time-consuming, calculations with a radiative transfer code, such as MODTRAN [Berk et al., 1998], in which A, B and C are computed for a wide range of atmospheric conditions (aerosol and water column amounts and different surface reflectance values). The calculations may be performed for each image to be analyzed, or may be performed ahead of time and stored in large look-up tables. The appropriate parameter values for the image are determined by fitting certain observed spectral features, such as water vapor absorption bands, to the calculations. For retrieving aerosol or haze properties such as the optical depth, methods are available that rely on “dark” pixels, consisting of vegetation or dark soil [Kaufman et al., 1997] or water bodies. Commonly used first-principles computer codes for atmospheric correction include: ATREM [Gao et al., 1996]; ACORN [R. Green, unpublished], available from Analytical Imaging and Geophysics LLC; FLAASH [Adler-Golden et al., 1999], developed by Spectral Sciences Inc. (SSI) and the Air Force Research Laboratory (AFRL); and ATCOR2 [Richter, 1996], used mainly for multispectral atmospheric correction.